Developing mathematical thinking through "low threshold – high ceiling" tasks Charlie Gilderdale NRICH Mathematics Project

Opposite Vertices

Opposite Vertices Challenge If I give you a line, can you tell me straight away if that line could be: the side of a square the diagonal of a square If such squares CAN be drawn, can you find an efficient method for drawing them?

Low threshold… Eight Hidden Squares Opposite Vertices Square It Square Coordinates

…High ceiling Vector Journeys We could move on to 3 dimensions… We could explore scalar products…

What’s new on NRICH? All new problems have Teachers’ NotesTeachers’ Notes Mapping documents have been updated Mapping documents New posters available, old posters updated Guidance on groupwork – see May 2010May 2010 More video support – see Tilted SquaresTilted Squares Upcoming themes on STEM and SportSTEM and Sport

Some final thoughts… NRICH views Mathematics as a creative discipline. In English lessons, students read novels, poems and plays but are also given opportunities to write for themselves. In Maths lessons, we expose students to interesting results and proofs, but we must also give them opportunities to create their own mathematical thinking, to work as mathematicians. NRICH tasks offer these opportunities.

“Maths is not just a spectator sport. It’s about participation and collaboration” NRICH Teachers’ Notes suggest how students can work in small groups without the need for teacher ‘interference’. The teacher’s role is as an observer with big ears and a small mouth, who is happy to stand back and let mistakes be made…

… but who draws the class’s attention to insights and thinking where appropriate and helps students to see how their discoveries fit into the bigger mathematical picture. This model of teaching offers the opportunity for lots of ‘lightbulb moments’ across the class rather than one lightbulb moment from a student that blinds everybody else!